The article reviews the experimental progress and theoretical interpretations of hidden-charm pentaquark and tetraquark states. It discusses the discovery of two hidden-charm pentaquark resonances, $P_c(4380)$ and $P_c(4450)$, by the LHCb Collaboration, which are beyond the quark model. The authors explore various theoretical frameworks to explain these states, including molecular schemes, dynamically generated resonances, QCD sum rules, and other models. They also review the experimental observations of charmonium-like $XYZ$ states, such as $X(3872)$, $Y(4260)$, and $Z^+(4430)$, and their decay patterns. The article highlights the puzzles and challenges in understanding these exotic states, emphasizing the need for future measurements to distinguish between different theoretical models. The review concludes with an outlook on the current status and future prospects of studying hidden-charm multiquark states.The article reviews the experimental progress and theoretical interpretations of hidden-charm pentaquark and tetraquark states. It discusses the discovery of two hidden-charm pentaquark resonances, $P_c(4380)$ and $P_c(4450)$, by the LHCb Collaboration, which are beyond the quark model. The authors explore various theoretical frameworks to explain these states, including molecular schemes, dynamically generated resonances, QCD sum rules, and other models. They also review the experimental observations of charmonium-like $XYZ$ states, such as $X(3872)$, $Y(4260)$, and $Z^+(4430)$, and their decay patterns. The article highlights the puzzles and challenges in understanding these exotic states, emphasizing the need for future measurements to distinguish between different theoretical models. The review concludes with an outlook on the current status and future prospects of studying hidden-charm multiquark states.